# Forecasting Technology of Sediment Transport

## Research content

This book simulates the sediment movement and calculates and forecasts the sedimentation in various port areas with the 2-D mathematical model of wave, current and sediment movement. The mathematical models used this time include the wind-wave model, tidal current model, sediment model and waterway siltation model. The brief introduction to these models will be presented in the following sections.

## Mathematical model of wind-wave field

1) Calculation method and equation

In recent years, the representative third-generation wind-wave generation and evolution direction spectrum model is more and more applied in projects. Therefore, the widely used SWAN model among the third-generation wind- wave models is used to simulate the wind-wave process near Tianjin Port. The SWAN model uses the action balance equation to describe the generation of wind-wave and its evolution in coastal areas [101, 102, 103, 104]. In the rectangular coordinate system, the action balance equation can be written as:

where *a* is the relative frequency of a wave (the frequency observed in the coordinate system moving with the water flow), *в* is wave direction (the direction perpendicular to crest line of waves in each spectral component), *C _{x}* and

*C _{y}* are the wave propagation in the

*x*and

*у*direction, and

*C*and

_{a}*C$*are the wave-propagation speed in the space

The first term at the left end of Eqn. (5.1) represents the rate of change of the spectral density over time, the second and the third terms represent the change of the spectral density during propagation in the geographic coordinate space, respectively; the fourth term represents the change of spectral density in the relative frequency *о* space due to changes in water depth and tidal current, and the fifth term represents the propagation of spectral density in the spectral-distribution direction *в* space (namely the refraction caused by the changes in water depth and tidal current).

The *S(a. 6)* at the right end of Eqn. (5.1) is the source term represented by the spectral density, including the wind-energy input, the non-linear interaction between waves and the energy dissipation caused by the wave breakage due to bottom friction, white-cap breaking and shallowing. It is also assumed that the terms can be linearly superimposed. The propagation speed in Eqn. (5.1) is calculated with the linear wave theory.

where *к = (k _{x}. k_{y})* is the wave number,

*d*is water depth,

*U = (U*is current velocity,

_{x},U_{y})*s*is space coordinate in the

*в*direction,

*m*is the coordinate perpendicular to

*s,*and the operator

*d/dt*is defined as gy =

*щ*+

*C ■*V

*'*

_{x>]y}.The SWAN model uses a fully-implicit finite-difference scheme, which is unconditionally stable and can have larger time step even in very shallow waters [101, 105, 106]. Discretize the action balance equation:

where *it* is the temporal-layer mark, *i _{x} ■ i_{y}*, v and

*i$*are the corresponding grid mark in the

*x, y. a*and

*в*direction,

*At. Ax, Ay, A о*and

*А в*are the time step, geographic space step, relative frequency step and direction distribution,

*n*is the number of iterations of each temporal layer.

*n** in the right-hand source terms of the equation is *n* or *n* — 1; *ц* 6 [0. 1], *v* 6 [0,1], the value of coefficient *у* and *v* decides whether the difference scheme of spectral space is an upwind scheme or central scheme and hence further decides the numerical discreteness and convergence in the spectral space and direction space. When ?/ = 0 or *v =* 0, it is a central difference scheme, the numerical discreteness tends to be zero, and the calculation accuracy is the highest. When // = 1 or *v* = 1, it is an upwind difference scheme, the numerical discreteness is the greatest, but the convergence is the best. One iteration and a four-times scanning technique is adopted in the calculation.

The computational domain boundary can be a land boundary or a water boundary. The land boundary does not generate waves, and it is considered that the incident wave can be absorbed without generating wave reflection. For the water boundary, the boundary conditions of the waveward side can be generally obtained from field observation or the numerical simulation of the wave model. Usually, the wave data of individual points can be obtained through field observation, and the wave data of coarse grid boundary can be obtained through other numerical model of large waves. Then the accuracy of the calculation result can be guaranteed within an acceptable error range.

The whole process of wind-wave from generation to growth then to attenuation during the strong wind process can be obtained by solving Eqn. (5.1). In the latest SWAN model, not only can the impact of water and submerged buildings (submerged levees) on the wave be simulated, but the diffraction can also be simulated by introducing an approximate calculation method.

In general, the latest SWAN model can give a reasonable near-shore wave field distribution with influence of buildings, and its simulation of wind-wave processes is not available in other models [107]. Therefore, it is reasonable to use the SWAN model to describe sedimentation near Tianjin Port.

2) Selection and grid partition of computational domain

To better reflect the change of the wind-wave field, the wind-waves are calculated by a three-layer nested model, namely a large model of the Bohai Sea and Yellow Sea, medium regional model of the Bohai Gulf and a small regional model at Tianjin Port.

During the calculation, it is considered that the land boundary does not generate waves, and incident waves can be absorbed without generating waves; the open boundary conditions of the medium model and small model are given in the form of spectra by the calculation result of the upper-layer model. This can solve the impact of the introduction of waves from external waters on the wave calculation of a small model.

The computational domain of each model is shown in Figures 5.1 through 5.3. The rectangular grid is adopted to divide the computational domain. The spacing of terrain grid of the large model is 6966 x 8767 m, the spacing of the

FIGURE 5.1: Isobath at Bohai Sea and Yellow Sea

FIGURE 5.2: Isobath at Bohai Gulf

terrain grid of medium model is 257 x 356 nr, and the spacing of terrain grid of small model is 93.75 x 85.375 m.

3) Verification of wave mathematical model

Due to the lack of measured wave data in the Tianjin Port area, we used the measured data of waves in the Huanghua Port area to verify the model. It is calculated that the SWAN mathematical model of waves can well describe the variation law of wave in the Huanghua Port area and the calculation

FIGURE 5.3: Isobath at Tianjin Port

result is feasible to provide hydrodynamic conditions for the sediment field. In view of the successful application of this wave model in the Huanghua Port, it should also be feasible to use this model for wave-field calculation at Tianjin Port.

## Numerical simulation of tidal current

Mike21 is standardized commercial software developed by the Danish Hydraulic Institute (DHI). It was developed on the basis of more than 20 years of continuous development and extensive engineering application experience worldwide. It is mainly used to simulate various current field issues (such as sea area, ports, bays and rivers) and environmental issues based on current fields (such as advection and diffusion of contaminants, water quality, heavy metals, sediment transport). Its application in numerous projects at home and abroad proved that it is highly precise, has good conservativeness and is convenient to use.

The numerical simulation of tidal current uses the Mike21 Flow Model module to build large and small two-layer models for calculation. The large model is Bohai Gulf model, and the small model is Tianjin Port area model. The large model provides the boundary conditions required by the hydrodynamic model for the small model to ensure that the local current field calculation near Tianjin Port conforms to the overall physical characteristics of tidal current field. The water-level boundary calculated with the China Sea tide model is adopted as the boundary condition of the large model [108, 109, 110]. 1) Mathematical model of tidal current

a) Calculation method and equation

The model adopts vertical average a 2-D shallow-water equation, the finite- difference method as the discrete method, and Alternating Direction Implicit (ADI) and Double Sweep (DS) as the calculation methods [111, 112, 113]. The basic equations are as follows:

Vertical average 2-D shallow-water equation:

Mass conservation equation:

Momentum equation:

where *h* is the water depth (unit: m); £ is the water-surface elevation (unit: m); *p* and *q* are the unit discharge in the *x* and *у* direction (unit: m^{3}/(s/m)); of which, *p = uh* and *q = vh; и* and *v* are the average current velocity along the water depth in the *x* and *у* direction; *C* is *Chezy* coefficient (unit: m^{1}^^{2}/s); *g* is gravity acceleration; / is wind friction coefficient; *V, V _{x}* and

*V*are wind speed and the component in the

_{y}*x*and

*у*direction (unit: m/s);

*W*is a Coriolis force parameter (unit: s

^{x});

*Pa*is atmospheric pressure (unit:

*kg/(m/s*is water density (unit:

^{2})); р_{ш }*kg/m*

^{3})*S,Si*and

_{X}*Siy*are negative source terms and the component in the

*x*and

*у*direction; and

*т*and

_{хх}. т_{ху}*т*are component of effective shear.

_{уу}b) Model range and computational domain

The computational domain of the large and small models is shown in Figure 5.4.

The calculation range of the large model is the entire Bohai Gulf, 102 *km* x

- 145.5
*km,*while the calculation range of small model is border of Bohai Gulf in the north to the location 10 km in the south to Duliujian River Estuary. Both models adopt square grids. The step of the grid of the large model is*Ax*=*Ay =*300*m*and the time step is 10 s. The step of the grid of the small model is*Ax = Ay*= 50*m*and the time step is 10 s. - c) Initial conditions and parameters

ф Initial conditions

FIGURE 5.4: Schematic diagram of computational domain of tidal current where: *£o(x,y,to),uo(x,y,to)* and vq(x, y, to) are the initial tide level and current velocity respective^. During the calculation, щ = 0 and vo = 0, and Co is the mean tide level of each boundary.

(2) Moving boundary and exposed beach treatment

The Mike21 Flow Model has good function to treat moving boundaries and can automatically judge whether the water depth of each unit meets the calculation condition according to the parameter setting. After commissioning, the dry and wet parameters were taken as 0.2 and 0.3, respectively.

*(3)* Parameter selection

The eddy viscosity coefficient in the model is 0.50, which is the DHI recommended value and the Manning Coefficient is 42.

2) Verification of tidal current field

The hydrological measurement data during two entire tidal cycles, namefy the spring tide from November 26 to 27, 2007, and the neap tide from December 4 to 5, 2007, was used for current field verification in this model. Figures

5.5 through 5.10 show the verification process lines of the tide level, current velocity and direction during these two hydrological full entire tidal cycles.

FIGURE 5.5: Comparison of measured and calculated water levels from November 26 to 27, 2007 (North N1)

FIGURE 5.6: Comparison of measured and calculated water levels from November 26 to 27. 2007 (South N1)

FIGURE 5.7: Comparison of measured and calculated current velocity and

direction from November 26 to 27, 2007 (*Continued)*

FIGURE 5.7 (Continued): Comparison of measured and calculated current velocity and direction from November 26 to 27, 2007

FIGURE 5.8: Comparison of measured and calculated water levels from

December 4 to 5, 2007 (North N1)

FIGURE 5.9: Comparison of measured and calculated water levels from December 4 to 5, 2007 (South N2)

FIGURE 5.10: Comparison of measured and calculated current velocity and direction from December 4 to 5, 2007 (*Continued)*

FIGURE 5.10 (Continued): Comparison of measured and calculated current velocity and direction from December 4 to 5, 2007

The verification results show that the calculated values and measured values at each measuring point are basically the same and the changes of tide level, current velocity and current direction are also basically consistent. Figures 5.11 through 5.14 show the current field at the time of flood maximum and ebb maximum and the isolines of current velocity at the time of flood maximum and ebb maximum. It can be seen that the tidal current field in the vicinity at Tianjin Port has the property of rectilinear current, and the tidal current moves towards the shore at the time of flood tide and offshore when the tide falls, and the tidal current basically moves in the WNW-ESE direction at high and low tide. It can also be concluded from the isoline of current velocity that the velocity of tidal current increases with increase of

FIGURE 5.11: Current field at the time of flood tide

FIGURE 5.12: Current field at the time of ebb tide

FIGURE 5.13: Isoline of current velocity at the time of flood tide

FIGURE 5.14: Isoline of current velocity at the time of ebb tide water depth, the velocity of flood tide is greater than that of falling tide, and the velocity of tidal current at the time of spring tide is greater than that at the time of neap tide. The tidal current field also accords with the law of tidal current movement in this sea area.

The tidal current movement simulated by the model satisfies the requirements that it should be similar to the actual tidal current feature, and more comprehensively reflects the regular pattern of tidal current movement in the vicinity of the Tianjin Port sea area. So it is reasonable to use the model in current field analysis of projects and further simulate the sediment movement in the area.